Bring down the polar regions.
https://en.wikipedia.org/wiki/Laurentide_Ice_Sheet
Earth used to be colder. Take the changes that occurred during the last glacial maximum and make them more extreme.
The average global temperature during the period known as the Last
Glacial Maximum from roughly 23,000 to 19,000 years ago was about 46
degrees Fahrenheit (7.8 degrees Celsius), some 13 degrees Fahrenheit
(7 Celsius) colder than 2019, the researchers said.
Certain regions were much cooler than the global average, they found.
The polar regions cooled far more than the tropics, with the Arctic
region 25 degrees Fahrenheit (14 degree Celsius) colder than the
global average.
During periods of cooling and also warming, changes are more extreme at the poles than closer to the equator. The equator does not change much. Average global temperature changes are driven mostly by changes in average temperature at very high latitudes.
You can achieve your 0C average by extrapolating the ice age to more southerly latitudes.
If this is just Earth, colder, then colder also means drier for most places where the average temperature does not change as much.
https://en.wikipedia.org/wiki/Last_Glacial_Maximum
The Amazon rainforest was split into two large blocks by extensive
savanna, and the tropical rainforests of Southeast Asia probably were
similarly affected, with deciduous forests expanding in their place
except on the east and west extremities of the Sundaland shelf. Only
in Central America and the Chocó region of Colombia did tropical
rainforests remain substantially intact – probably due to the
extraordinarily heavy rainfall of these regions.
A map of vegetation patterns during the last glacial maximum. Most of
the world's deserts expanded...
In Australia, shifting sand dunes covered half the continent, while
the Chaco and Pampas in South America became similarly dry.
Present-day subtropical regions also lost most of their forest cover,
notably in eastern Australia, the Atlantic Forest of Brazil, and
southern China, where open woodland became dominant due to drier
conditions. In northern China – unglaciated despite its cold climate –
a mixture of grassland and tundra prevailed, and even here, the
northern limit of tree growth was at least 20° farther south than
today.